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arXiv · 2604.17682

Thermodynamic behavior of cosmological models with fractional entropy

Miguel Cruz·Diego da Silva·Simón González·Samuel Lepe·Joel Saavedra·Manuel Gonzalez-Espinoza
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Abstract

We investigate the thermodynamic and phenomenological implications of a cosmological model governed by fractional entropy applied to the apparent horizon of a flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) universe. By utilizing the unified first law of thermodynamics alongside the Kodama-Hayward temperature, we derive a generalized set of Friedmann equations characterized by a fractional parameter $\alpha \in (1,2]$. The thermodynamic analysis reveals that the specific heats $C_V$ and $C_p$ share the same sign and depend solely on the deceleration parameter, demonstrating that the fractional model is thermodynamically stable during the late-time accelerated expansion and does not exhibit phase transitions. To constrain the background dynamics, we confront the truncated fractional model with a joint sample of late-time observational data, including Cosmic Chronometers, Pantheon+SH0ES supernovae, and the latest DESI DR2 Baryon Acoustic Oscillations. Exploring the physically motivated range $1<\alpha\le 2$, we find that the fit quality degrades monotonically as $\alpha$ decreases from the General Relativity limit. Rather than limiting the model's physical value, this demonstrates its theoretical robustness: the fractional framework acts as a continuous deformation parameter that preserves macroscopic thermodynamic stability. The data favors $\alpha$ close to 2 (yielding $H_0=69.50\pm 0.42$ km/s/Mpc and $\Omega_{m0}=0.292\pm 0.008$), revealing that while the late-time background expansion strongly constrains deviations from the standard area law, the fractional model smoothly and stably accommodates these constraints without exhibiting thermodynamic pathologies.

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Miguel Cruz, Diego da Silva, Simón González, Samuel Lepe, Joel Saavedra, Manuel Gonzalez-Espinoza. 2026-04-20. Thermodynamic behavior of cosmological models with fractional entropy. https://doi.org/10.1016/j.nuclphysb.2026.117616

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